Finite Group Databasebeta

← #26012924⋊C3 #45686303

Subgroups — #26012924⋊C3 #45686303

Order 33300.

224 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C3⋊(C5⋊(D37⋊C3))C212yesmaximal, complemented
2C3×C5⋊D5×C37⋊C3C211yesmaximal, characteristic, complemented
3#26012924C311yesmaximal, characteristic, complemented
4(C5⋊(D37⋊C3))⋊D5—31nomaximal
5C3×C52×C37⋊C3C2211yescharacteristic, complemented, Hall
6D5×C3⋊(D37⋊C3)—52nomaximal
7C5×D555C2×C312yescomplemented
8C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
9C5⋊D5×C37⋊C3—21no—
10C5⋊D5×C37⋊C3D311yescharacteristic, complemented
11C5×C5⋊(D37⋊C3)—32no—
12(C5⋊D5)⋊D37—31noHall
13C3⋊(C5⋊(D37⋊C3))D512yescomplemented
14C5×C3⋊(D37⋊C3)—52no—
15C3×D5×C37⋊C3—52no—
16C3×D5×C37⋊C3—102no—
17C52×C37⋊C3—21no—
18C52×C37⋊C3C2×D311yescharacteristic, complemented
19C3×C52×C37C22×C311yescharacteristic, complemented
20D5×D111—52no—
21D5×D37⋊C3—152no—
22C37×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D185—32no—
24C3×C5×C37⋊C3—22no—
25C3×C5×C37⋊C3C2×D512yescomplemented
26C2×C3⋊(D37⋊C3)—251noHall
27D555C3×D512yescomplemented
28C5×D111—52no—
29C3×D5×C37—52no—
30C3×D5×C37—102no—
31C5⋊(D37⋊C3)—32no—
32D5×C37⋊C3—52no—
33D5×C37⋊C3—102no—
34D5×C37⋊C3—102no—
35D5×C37⋊C3—104no—
36C5×D37⋊C3—152no—
37C52×C37C2×C3×D311yescharacteristic, complemented, Hall
38C3×D15⋊D5—371nomaximal, Hall
39D5×D37—152no—
40C2×C3×C37⋊C3—251no—
41C3⋊(D37⋊C3)—52no—
42C3×C5×C37—22no—
43C3×C5×C37C2×C3×D512yescomplemented
44C5×C37⋊C3—24no—
45C5×C37⋊C3—22no—
46C5×C37⋊C3—22no—
47C5×C37⋊C3D3×D512yescomplemented
48C3×C5×D15—372no—
49C32×C5⋊D5—371no—
50C2×D111—251no—
51C2×D37⋊C3—751no—
52D185—32no—
53C5×D37—152no—
54D5×C37—52no—
55D5×C37—102no—
56C3×C37⋊C3D5211yescharacteristic, complemented, Hall
57D15⋊D5—371no—
58C3×D52—1111no—
59C32×C52—371noHall
60C2×C3×C37—251no—
61D111—52no—
62C2×C37⋊C3—251no—
63C2×C37⋊C3—501no—
64D37⋊C3—152no—
65C5×C37—22no—
66C5×C37C3×D3×D512yescomplemented
67C3×D3×D5—1852no—
68C5×D15—372no—
69C3×C5⋊D5—371no—
70C3×C5⋊D5—741no—
71C3×C5⋊D5D37⋊C311yescharacteristic, complemented
72C3×C5×D5—1112no—
73C2×D37—751noHall
74C3×C37C3×D5211yescharacteristic, complemented
75C37⋊C3—21no—
76C37⋊C3D15⋊D511yescharacteristic, complemented
77D52—1111noHall
78C3×D15—372no—
79C3×C5×D3—1852no—
80C32×D5—3702no—
81C32×D5—1852no—
82C3×C52—371no—
83C3×C52—741no—
84C3×C52C2×D37⋊C311yescharacteristic, complemented
85C2×C37—251no—
86D37—152no—
87C2×C3×D5—5552no—
88D3×D5—1852no—
89C5⋊D5C3⋊(D37⋊C3)11yescharacteristic, complemented
90C5×D5—1112no—
91C32×C5—372no—
92C32×C5—742no—
93C37C3×D15⋊D511yescharacteristic, complemented, Sylow
94C2×C3×D3—9251noHall
95C2×C3×C5—5552no—
96D15—372no—
97C3×D5—52no—
98C3×D5—102no—
99C3×D5—1112no—
100C3×D5—3702no—
101C3×D5—3704no—
102C3×D5—3702no—
103C3×D5—1852no—
104C5×D3—1852no—
105C52C2×C3⋊(D37⋊C3)11yescharacteristic, complemented, Sylow
106C2×D5—5552no—
107C2×C32—9251no—
108C3×D3—1852no—
109C3×C5—22no—
110C3×C5—372no—
111C3×C5—742no—
112C3×C5—744no—
113C3×C5—742no—
114C3×C5D5×D37⋊C312yescomplemented
115C22×C3—27751no—
116C2×D3—9251no—
117C2×C5—5552no—
118D5—52no—
119D5—102no—
120D5—1112no—
121C32—371noSylow
122C2×C3—251no—
123C2×C3—5552no—
124C2×C3—18501no—
125C2×C3—9251no—
126D3—1852no—
127C5—22no—
128C5D5×C3⋊(D37⋊C3)12yescomplemented
129C22—27751noSylow
130C3—371no—
131C3—741no—
132C3(C5⋊(D37⋊C3))⋊D511yescharacteristic, complemented
133C2—251no—
134C2—5552no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C37C22×C3
LCSG ▷ C3×C52×C37
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×C3⋊(C5⋊(D37⋊C3))C2semidirect
2. C3×C5⋊D5×C37⋊C3C2semidirect
3. #26012924C3semidirect
5. C3×C52×C37⋊C3C22semidirect
7. C5×D555C2×C3semidirect
8. C3×C37×C5⋊D5C2×C3semidirect
10. C5⋊D5×C37⋊C3D3semidirect
13. C3⋊(C5⋊(D37⋊C3))D5semidirect
18. C52×C37⋊C3C2×D3semidirect
19. C3×C52×C37C22×C3semidirect
22. C37×C5⋊D5C3×D3semidirect
25. C3×C5×C37⋊C3C2×D5semidirect
27. D555C3×D5semidirect
37. C52×C37C2×C3×D3semidirect
43. C3×C5×C37C2×C3×D5semidirect
47. C5×C37⋊C3D3×D5semidirect
56. C3×C37⋊C3D52semidirect
66. C5×C37C3×D3×D5semidirect
71. C3×C5⋊D5D37⋊C3semidirect
74. C3×C37C3×D52semidirect
76. C37⋊C3D15⋊D5semidirect
84. C3×C52C2×D37⋊C3semidirect
89. C5⋊D5C3⋊(D37⋊C3)semidirect
93. C37C3×D15⋊D5semidirect
105. C52C2×C3⋊(D37⋊C3)semidirect
114. C3×C5D5×D37⋊C3semidirect
128. C5D5×C3⋊(D37⋊C3)semidirect
132. C3(C5⋊(D37⋊C3))⋊D5semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×C3⋊(C5⋊(D37⋊C3))2
C3×C5⋊D5×C37⋊C32
#260129243
(C5⋊(D37⋊C3))⋊D53
D5×C3⋊(D37⋊C3)5
C3×D15⋊D537